How can I evenly split a cube?
If you say the knife does not work for you, as it only cuts the surface, then you may want to use the option Z to Cut Through, for a snapping on angles to ensure a clean cut, you can also use C, so a cut from the front or any orthogonal view can be made in a straight line.

Here the optional functions of the knife tool:


A cut through cube:


Another option would be to use bisect, where you can also find some optional functionality mentioned while the tool is active.

Here a bisect example, bisect has the advantage that you can select the fill option and it will generate a surface that closes the cut:


I believe bisect might be a good idea as you can adjust not only the direction but also the position interactively.

Happy Blending.